Kit Fine; XIV*—Ontological Dependence, Proceedings of the Aristotelian Society, Volume 95, Issue 1, 1 June 1995, Pages 269–290, https://doi.org/10.1093/aristote.

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

Ontological dependence is a relation—or, more accurately, a family of relations—between entities or beings. For there are various ways in which one being may be said to depend upon one or more other beings, in a sense of “depend” that is distinctly metaphysical in character and that may be contrasted, thus, with various causal senses of this word. More specifically, a being may be said to depend, in such a sense, upon one or more other beings for its existence or (...) for its identity. Some varieties of ontological dependence may be analyzed in modal terms—that is, in terms of distinctly metaphysical notions of possibility and necessity—while others seem to demand an analysis in terms of the notion of essence. The latter varieties of ontological dependence may accordingly be called species of essential dependence. Notions of ontological dependence are frequently called upon by metaphysicians in their proposed analyses of other metaphysically important notions, such as the notion of substance. (shrink)

The purpose of the book is to clarify the notion of existential dependence and cognate notions, such as supervenience and the notion of an internal relation. I defend the view that such notions are best understood in terms of the concept of metaphysical grounding, i.e. the concept of one fact obtaining in virtue of other facts, where ‘in virtue of’ has a distinctively metaphysical meaning.

General discussion of grounding, including its formal features, relations to other notions, and applications.

Consider a circle and a pair of its semicircles. Which is prior, the whole or its parts? Are the semicircles dependent abstractions from their whole, or is the circle a derivative construction from its parts? Now in place of the circle consider the entire cosmos (the ultimate concrete whole), and in place of the pair of semicircles consider the myriad particles (the ultimate concrete parts). Which if either is ultimately prior, the one ultimate whole or its many ultimate parts?

This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, (...) I outline a different approach, which circumvents these problems by dispensing with the priority or dependence relation altogether. Along the way, I show how this approach enables the mathematical structuralist to defuse an objection recently raised against her view. (shrink)

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set (...) theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science. (shrink)

I address an intuition commonly endorsed by metaphysicians, that there must be a fundamental layer of reality, i.e., that chains of ontological dependence must terminate: there cannot be turtles all the way down. I discuss applications of this intuition with reference to Bradley’s regress, composition, realism about the mental and the cosmological argument. I discuss some arguments for the intui- tion, but argue that they are unconvincing. I conclude by making some suggestions for how the intuition should be argued for, (...) and discussing the ramifications of giving the justification I think best. (shrink)

I explain why Ross Cameron's definition of ultimate ontological basis is incorrect, and propose a different definition in terms of ontological dependence, as well as a definition of reality's fundamental layer. These new definitions cover the conceptual possibility that self-dependent entities exist. They also apply to different conceptions of the relation of ontological dependence.